Micro, nano, and pico are all SI prefixes for units of measurement (see the bottom of my post) that so many companies bastardize to sound cool... which is the case in the aquarium hobby.
The term Nano undoubtedly came on the aquarium market as a product name for one of the all-in-one small units we currently have (I would guess JBJ was the first, but I can't find proof of that online and they came out before I started in the hobby). I would have to say that Pico definitely started the same way with the picotope (as James already said). The confusion now comes in with people calling any tank smaller than 30 gallons a nano.
I generally think of Nano as a name for any self-contained all-in-one tank, not just a small fish tank. I'm not saying I'm right, but I am saying it leads to confusion any other way. I'll make an analogy to "nose wiping paper." If I ask for a kleenex, you're probably going to immediately think to give me a sheet of tissue from a box on a table whether it is a kleenex brand or not. You probably wouldn't run into your bathroom and get a sheet of tissue from the roll near the toilet... even though they are very similar and either would work.
To make it most simple...
You say you have a nano, I think of an all-in-one unit under 30 gallons. You say you have a pico, you have an all-in-one of 3 gallons or less. Otherwise, you say you have a XX gallon tank and I think of a tank with silicon on all 4 corners.
SI Unit Prefixes
10^15 peta
10^12 tera
10^9 giga
10^6 mega
10^3 kilo
10^2 hecto
10^1 deca
10^0 (none)
10^−1 deci
10^−2 centi
10^−3 milli
10^−6 micro
10^−9 nano
10^−12 pico
10^−15 femto
Some fun measurement facts:
Red blood cells are 7 micrometers in diameter.
Human hair is 100 micrometers in diameter.
The pits on a CD are approx. 100 nanometers deep by 500 nm wide.
A DNA double helix is about 2 nm wide.
A helium atom is roughly 31 picometers in diameter (including the electron cloud).
The highest resolution electron microscope has a resolution down to 50 pm.
The first 2 terabyte computer hdd's came on the market this year. That's 2000 gigabytes. In 1999, the biggest drives available were less than 100 gb's.